منابع مشابه
Deformations of Border Bases
Border bases have recently attracted a lot of attention. Here we study the problem of generalizing one of the main tools of Gröbner basis theory, namely the flat deformation to the leading term ideal, to the border basis setting. After showing that the straightforward approach based on the deformation to the degree form ideal works only under additional hypotheses, we introduce border basis sch...
متن کاملSubideal border bases
In modeling physical systems, it is sometimes useful to construct border bases of 0-dimensional polynomial ideals which are contained in the ideal generated by a given set of polynomials. We define and construct such subideal border bases, provide some basic properties and generalize a suitable variant of the Buchberger-Möller algorithm as well as the AVI-algorithm of [5] to the subideal settin...
متن کاملToric Border Bases
We extend the theory and the algorithms of Border Bases to systems of Laurent polynomial equations, defining “toric” roots. Instead of introducing new variables and new relations to saturate by the variable inverses, we propose a more efficient approach which works directly with the variables and their inverse. We show that the commutation relations and the inversion relations characterize tori...
متن کاملModule Border Bases
In this paper, we generalize the notion of border bases of zerodimensional polynomial ideals to the module setting. To this end, we introduce order modules as a generalization of order ideals and module border bases of submodules with finite codimension in a free module as a generalization of border bases of zero-dimensional ideals in the first part of this paper. In particular, we extend the d...
متن کاملNotes on Stable Border Bases
Given X, a set of points whose coordinates are perturbed by errors, we want to determine a “numerically stable” basis B of the vanishing ideal I(X), i.e. for any permitted perturbation X̃ of the original set of points X, only slight changes to the coefficients in B are needed to produce a basis B̃ for the perturbed vanishing ideal I(X̃). We use border bases because they exhibit good numerical stab...
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ژورنال
عنوان ژورنال: Collectanea mathematica
سال: 2008
ISSN: 0010-0757
DOI: 10.1007/bf03191188